System MGRS (Military Grid Reference System) identifying and reporting location
This system assigns a code („geocode”) to every geographic point and identifies it for military or navigation purposes, with a high degree of accuracy. It is based on the UTM map coordinate system on the one hand, and on the partition of the UTM zones into geographic quadrangles of 6°x8° on the other hand. It gives a possibility to appoint an Earth’s point with an accuracy of 1m.
A UTM zone of 6° represents a territory which is about 667 km wide by the Equator. The mid-meridian of the zone corresponds to the UTM’s Y coordinate-line of 500000 m, and four columns with a width of 100000 m, both westwards and eastwards, cover the whole zone. On the other hand, the zone is partitioned into rows with a width of 100000 m by X coordinate lines parallel with the Equator (XUTM=0.0 m). The columns and rows together create a grid of 100kmx100km. This partition is independent of the partition into geographic quadrangles of 6°x8° mentioned above.
The UTM zones of 6° with its 800 km wide grid are grouped in sets of three, and the 3x8 columns of 100000 m are denoted eastwards by the capital letters of the English alphabet from A to Z (I and O are removed). The notation of the 100 rows with a width of 100000 m comes true in each zone both northwards and southwards by the capital letters of the English alphabet. In the zones with odd serial number, the rows are denoted by the letters from A to V (I and O removed), starting from the Equator in both directions, recurrently 5 times up to the poles. In the zones with even serial number, the notation of the rows: FGHJ…UVABCDE (I and O removed), starting from the Equator in both directions, recurrently 5 times up to the poles.
The MGRS identifier is composed of three parts:
- the identifier of the geographic quadrangle of 6°x8° (serial number of the zone + key-letter of the band, e.g. 34T);
- the identifier of the square of 100 km x 100 km (key-letter of the column + key-letter of the row, e.g. CT)
- the last five numbers of the UTM coordinates rounded to meters, inside of the square of 100 km x 100 km (coordinate Y + coordinate X, alltogether 10 digits, e.g. 34T CT 54053 59662).
Reversaly, the UTM coordinates can be restored based on the MGRS identifier: the UTM coordinates of the lower left corner rounded to 100000 m can be determined from the identifier of the square of 100kmx100km, and the following 2x5 figures provide the last 5 digits of the UTM coordinates.
The territory of Hungary takes up its position on the eastern edge of the merged 31-33 zones, in the columns marked by W, X and Y, and in the rows marked by L, M, N and P, in addition on the western edge of the merged 34-36 zones, in the columns marked by B, C, D, E and F, and in the rows marked by R, S, T, U and V.
Exercise:
Ankara, Kizilay Meydani WGS84 coordinates: F = 39.920766° = 39° 55' 14.7576"
L = 32.85411° = 32° 51'14.796"
serial number of the zone: 36 (longitude of the point is between 30°E and 36°E)
key-letter of the band: S (latitude of the point is between 32°N and 40°N)
code of the map sheet 6°x8°: 36 S
midmeridian of the zone: L0 = 33°
arc (L-L0) = arc(32.85411°-33.0°) = -0.00254626
UTM coordinates:
A0 = 4420731.291m (by the Simpson’s rule with n=8)
(A0 » 4420709.606m by the Simpson’s rule with n=2)
A1 = 4898357.961
A2 = 1571705.840
A3 = 145891.7889
A4 = 334005.2144
A5 = -100441.5023
(Y =) Easting = 0.9996*A1*(-0.00254626) + 0.9996*A3*(-0.00254626)3 +
+ 0.9996*A5*0.002546265+ 500000 = -12467.508m + 0.0024m – 0.00000001m + 500000m =
= 487532.49m
(X =) Northing = 0.9996*A0 + 0.9996*A2*(-0.00254626)2 + 0.9996*A4*(-0.00254626)4 =
= 4418962.998 + 10.186 + 0.000014 = 4418973.18m
MGRS code: 36 S V K 87532 18973